Current reinforcement model reproduces center‐in‐center vein trajectory of Physarum polycephalum

• Published in: Development, growth & differentiation Vol. 59; no. 5; pp. 465 - 470
• Main Authors: Akita, Dai, Schenz, Daniel, Kuroda, Shigeru, Sato, Katsuhiko, Ueda, Kei‐ichi, Nakagaki, Toshiyuki
• Format: Journal Article
• Language: English
• Published: Japan Wiley Subscription Services, Inc 01.06.2017
• Subjects: Adaptability; current reinforcement; mathematical model; Mathematical models; Models, Biological; Morphogenesis; Physarum polycephalum; Physarum polycephalum - physiology; slime mold; Temporal variations; Veins; mathematical model; slime mold; current reinforcement
• ISSN: 0012-1592; 1440-169X
• DOI: 10.1111/dgd.12384

Vein networks span the whole body of the amoeboid organism in the plasmodial slime mould Physarum polycephalum, and the network topology is rearranged within an hour in response to spatio‐temporal variations of the environment. It has been reported that this tube morphogenesis is capable of solving mazes, and a mathematical model, named the ‘current reinforcement rule’, was proposed based on the adaptability of the veins. Although it is known that this model works well for reproducing some key characters of the organism's maze‐solving behaviour, one important issue is still open: In the real organism, the thick veins tend to trace the shortest possible route by cutting the corners at the turn of corridors, following a center‐in‐center trajectory, but it has not yet been examined whether this feature also appears in the mathematical model, using corridors of finite width. In this report, we confirm that the mathematical model reproduces the center‐in‐center trajectory of veins around corners observed in the maze‐solving experiment. The thick veins tend to trace the shortest possible route by turning at the corners of corridors following a center‐in‐center trajectory. This process of vein morphogenesis is based on the phenomenological rule of current reinforcement: a vein becomes thicker as protoplasmic streaming is stronger, and dies out otherwise. By means of this mathematical modeling, we confirmed the center‐in‐center trajectory of vein developed when turning at a corner as actually observed in the maze‐solving experiment.